Yibum is not like gilgul because it is for a different reason. When it comes to the rest of the sins of the Torah, rectification can be achieved through suffering in this world and after death in Gehinom (Purgatory). Thus, not all sparks of the Nefesh need to reincarnate, but they may come back only as an ibur of the type mentioned in the previous section. Only specific sparks actually reincarnate.
Rectification can be achieved through suffering, or through the performance of mitzvot. The Rav is concentrating on rectification through suffering, it seems, because of what he wants to say here about yibum.
We also learned in the last section that completely rectified sparks do not need to reincarnate, and those that are mostly rectified, but not completely, will reincarnate as an ibur from birth. Only specific sparks that are badly damaged, or have not yet undergone any tikun through gilgul, will reincarnate to become the main soul of the body. The entire nefesh that was in the first body must return again for its own sake
However, yibum occurs because the person died before having children, a lack of success that makes it as if he never came into the world, as if his first body did not exist at all, as it says in the Zohar (Vayashev 187a).
The man left this world without leaving behind any progeny, and therefore it is as if he never existed.
Therefore, the entire Nefesh that was in the first body must return again for its own sake.
This is the main point here. Rectification through suffering did not happen in the first body, and no parts of the soul were released from the cycle of gilgul.
In the end, it is the second body that becomes his main one. After rectification and death in this world the Nefesh will resurrect only in this second body. There will be no soul to enter the first body, other than the "Ruach [spirit] that he put into his wife", as it says in Sabba of [Zohar] Mishpatim.
When a man first procreates with his wife, a part of his soul goes into the woman and remains there in her womb. This is the spirit that the husband has left within his wife. It is only this minimal spirit that is available to resurrect the body. (See Chapter 36.)
This is the difference between someone who has died without leaving children and must return in the secret of Yibum, and one who dies with sins and must reincarnate.
All the details we have explained regarding the sparks of the Nefesh apply as well to Ruach and Neshama.
[Commentary by Shabtai Teicher.]